Online Computer Terms Dictionary - C

cyclic redundancy check

<algorithm> (CRC or "cyclic redundancy code") A number derived from, and
stored or transmitted with, a block of data in order to detect corruption. By
recalculating the CRC and comparing it to the value originally transmitted, the
receiver can detect some types of transmission errors.

A CRC is more complicated than a checksum. It is calculated using division
either using shifts and exclusive ORs or table lookup (modulo 256 or 65536).

The CRC is "redundant" in that it adds no information. A single corrupted bit in
the data will result in a one bit change in the calculated CRC but multiple
corrupted bits may cancel each other out.

CRCs treat blocks of input bits as coefficient-sets for polynomials. E.g.,
binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 +
0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial". A second polynomial,
with constant coefficients, is called the "generator polynomial". This is
divided into the message polynomial, giving a quotient and remainder. The
coefficients of the remainder form the bits of the final CRC. So, an order-33
generator polynomial is necessary to generate a 32-bit CRC. The exact bit-set
used for the generator polynomial will naturally affect the CRC that is
computed.

Most CRC implementations seem to operate 8 bits at a time by building a table of
256 entries, representing all 256 possible 8-bit byte combinations, and
determining the effect that each byte will have. CRCs are then computed using an
input byte to select a 16- or 32-bit value from the table. This value is then
used to update the CRC.

Ethernet packets have a 32-bit CRC. Many disk formats include a CRC at some
level.